Nonlinear behavior of gelatin networks reveals a hierarchical structure

We investigate the strain hardening behavior of various gelatin networks-namely physical gelatin gel, chemically cross-linked gelatin gel, and a hybrid gel made of a combination of the former two-under large shear deformations using the pre-stress, strain ramp, and large amplitude oscillations shear protocols. Further, the internal structures of physical gelatin gels and chemically cross-linked gelatin gels were characterized by small angle neutron scattering (SANS) to enable their internal structures to be correlated with their nonlinear rheology. The Kratky plots of SANS data demonstrate the presence of small cross-linked aggregates within the chemically cross-linked network whereas, in the physical gelatin gels, a relatively homogeneous structure is observed. Through model fitting to the scattering data, we were able to obtain structural parameters, such as the correlation length (ξ), the cross-sectional polymer chain radius (Rc) and the fractal dimension (df) of the gel networks. The fractal dimension df obtained from the SANS data of the physical and chemically cross-linked gels is 1.31 and 1.53, respectively. These values are in excellent agreement with the ones obtained from a generalized nonlinear elastic theory that has been used to fit the stress-strain curves. The chemical cross-linking that generates coils and aggregates hinders the free stretching of the triple helix bundles in the physical gels.

Espectroscopía de emisión de rayos x. Aplicación a la caracterización de materiales. X-ray emission spectroscopy. Application to materials characterization

La idea principal del proyecto abarca el estudio de parámetros y fenómenos físicos. Los avances logrados se aplicarán al desarrollo de software y metodologías para cuantificación de materiales mediante microanálisis con sonda de electrones y microscopía electrónica de barrido. El microanálisis no es una técnica absoluta, sino que requiere de estándares de referencia, para obviar el uso de ciertos parámetros geométricos y atómicos difíciles de conocer con una precisión adecuada. Para contar con un método sin estándares debe abordarse la determinación de parámetros atómicos e instrumentales, que es uno de los aspectos que se desea encarar en este proyecto. Por otro lado, también se pretende incluir los parámetros estudiados en un software de cuantificación desarrollado por integrantes del proyecto. Otro de los propósitos del plan de trabajo es estudiar la potencialidad de la resolución espacial de una microsonda de electrones con el fin de desarrollar una metodología para caracterizar interfases, bordes de granos e inclusiones, con resolución submicrométrica, ya que los métodos tradicionales de cuantificación se restringen al caso de muestras planas y homogéneas dentro del volumen de interacción, pero la caracterización de inhomogeneidades a nivel micrométrico no ha sido desarrollada todavía, salvo algunas excepciones. The main idea of this project involves the study of physical parameters and phenomena. The concretion of the different goals will permit the elaboration of softeare and methodologies for materials characterization by means of electron probe microanalysis and scanning microscopy. Electron probe microanalysis is not an absolute technique, but requires reference standards in order not to involve certain geometrical and atomic parameters for which high uncertainties cannot be avoided. In order to have standardless method, the determination of atomic and instrumental parameters must be accomplished, as will be faced through this project. Complementary, the parameters studied will be included in a quantification software developed in our research group of FaMAF. Another objective of this activity plan is to study the spatial resolution potentiality of a focalized electron beam, with the aim of characterizing interphases, grain boundaries and inclusions with submicron sensitivity, since the traditional quantification procedures are restricted to flat homogeneous samples, whereas the characterization of inhomogeneities has not been developed yet.

Nonlinear analysis and control of PEM fuel cells

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2010

Approximations of the Fisher information for the construction of efficient experimental designs in nonlinear mixed effects models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

equivalence of almost bent and almost perfect nonlinear functions and their generalizations

Vectorial Boolean function, almost bent, almost perfect nonlinear, affine equivalence, CCZ-equivalence

Theory and application of nonlinear wave propagation phenomena in combined reaction/separation processes

Reaction separation processes, reactive distillation, chromatographic reactor, equilibrium theory, nonlinear waves, process control, observer design, asymptoticaly exact input/output-linearization

Sparse nonlinear discriminants

Kernel-Functions, Machine Learning, Least Squares, Speech Recognition, Classification, Regression

Analysis of the potential of nonlinear solvent gradients in preparative chromatography

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2010

Study of human brain metabolites using magnetic resonance spectroscopy methods at 7 TESLA

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2012

Nonlinear frequency response analysis for the diagnosis of polymer electrolyte membrane fuel cells

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2012

The investigation of glutamine and glutamate in the human brain using MR spectroscopy at 7 Tesla

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2014

Nonlinear dynamics of Poly(hydroxyalkanoate) production in Ralstonia eutropha and Rhodospirillum rubrum

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

A nonlinear threshold model for the dependence of extremes of stationary sequences

One of the main implications of the efficient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stocks prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example. JEL classification: C12; C15; C22; C51 Keywords and Phrases: asymmetries, crises, extreme values, hypothesis testing, leverage effect, nonlinearities, threshold models